This book explores number
sentences as it investigates many different ways to reach the number
11.

Have students pick a number.
Have them write as many different number sentences as possible. Encourage
students to use more than two numbers, more than one operation, and
to write the sentences using the correct order of operations.

Hulme, Joy N.
Sea Sums. New York; Hyperion Books for Children, 1996.

Addition and subtraction
problems are told in an ocean theme.

Have students create
a book of their own along the same lines, writing number sentences
to describe the pages of their book. Also, the ideas for use with
12 Ways to Get 11 are appropriate here.

Dee, Ruby. Two
Ways to Count to Ten. New York: Henry Holt and Company, 1988.

The leopard king is seeking
a husband for his daughter. The animal who is able to toss a spear into
the air and count to ten before it hits the ground wins. This tale indicates
that sometimes the cleverest is the winner.

Before reading the book,
have students try to count to twenty as fast as possible and record
the times. After reading the book, connect the different ways to count
to a number to the factors of the number.

Many favorite fairy tales
are told from a more modern perspective. Particular stories that emphasize
patterns are The Princess and the Bowling Ball, Jacks
Story, and The Stinky Cheese Man.

After reading all of
these books, give children a strip of adding machine tape. Have them
draw a pattern on their strip, making sure they draw at least two
cycles of their pattern. Then have the children sort their patterns
on the classroom wall so that like patterns are grouped together.
Children need to justify why patterns in a group are alike and identify
the pattern as ABAB, etc. (This activity is described more fully in
the NCTM Addenda Series Patterns K-6.)

A wide range of mathematics
topics are illustrated through diagrams. The section on The Magic Machine
deals with ideas connected to a function machine. The section on Counting
with Circles provides a nice introduction to ideas connected with variables.

Read the pages in the
section on The Magic Machine. Have children identify what each machine
does. Then have children create their own function machine.
Read the section on Counting with Circles. Have students create similar
pages of their own.

Each page of this book contains
several problems, with multiplication as the focus.

Take any page of the book.
Create a table to illustrate the relationships that are described.
Try to write one or more rules for the relationships. Graph the results.
Connect the steepness of the graphs to ideas of slope.

Hulme, Joy N. Sea
Squares. New York: Hyperion Books, 1991.

This counting book uses an
ocean theme as it explores multiplication patterns of the form n x n,
from 1 x 1 to 10 x 10.

Have children consider
the next few numbers in the pattern. Have children write a rule to
describe their pattern. If appropriate, introduce the notation for
exponents.

A jar contains an island
on which are two countries. Each country contains three mountains. The
patterns continue until there are 10! jars.

Have children relate the
descriptions in the book to multiplication. If appropriate, introduce
factorial notation. Have children create their own multiplication
book. Relate the ideas in the book to problems connected with the
Multiplication Counting Principle. [e.g., Nine people are on a baseball
team. Without any restrictions, how many batting orders are possible?

Goble, Paul. Her
Seven Brothers. New York: Aladdin Paperbacks, 1988.

A young girl searches for
seven brothers she does not know. Through a series of adventures, they
become the Big Dipper. The story is based on a Cheyenne legend.

Have children create
designs using colored toothpicks. Have them describe the number of
toothpicks of a given color needed for 1, 2, 3, 4, ..., 100 of their
designs. Write a rule that tells a company how many colored toothpicks
they need to have if someone orders a given number of your design.
(Activities with sample childrens work are described in a chapter
by Thompson, Chappell, and Austin in the forthcoming Addenda series
on Changing the Faces of Mathematics: Perspectives on Indigenous Peoples.)

A couple finds a brass pot
which doubles everything placed into it. The couple's life changes dramatically.

Suppose you start with
5 coins and place them in the pot. Continue doubling the results and
record the values in a table. How long will it take before you have
1000 coins? What if you had a triple pot? What if you started with
1000 coins and had a half-pot? How long would it take before you have
less than 50 coins?

If the pattern continues,
how many ants would be needed for the next three food items? Find
the total number of ants each time a new food is added to the story.
Try to write rules to describe your patterns. Graph the number of
ants with each food and the total number of ants.

A wise man does a service
for a king who insists on giving a reward. The wise man requests one
grain of rice for the first square of a chessboard, with the number
of grains doubling for each new square of the chessboard. The king eventually
realizes that there would not be enough rice in all the world to meet
the wise man's request.

A young girl heals the rajah's
sick elephants. She then defeats the rajah by requesting a reward of
rice in which the number of grains doubles each day until all the squares
of a chessboard are covered.

Demi. One Grain
of Rice: A Mathematical Folktale. New York: Scholastic, Inc., 1997.

A young girl uses her wits
to help starving people and teach the wicked rajah a lesson. This is
another variant on the doubling tale.

A humble servant gets one
grain of rice on the first day from the Emperor, with the number of
grains of rice set to double each day for 100 days.

For all four of these
books, have children create a table with the number of grains of rice
on each square of the chessboard or each day of the specified period.
Have children describe the patterns they see and graph the results,
if possible. Have children explore weight and space issues connected
to the quantities of rice.

This retelling of the classic
three little pigs story has a Hawaiian flavor.

Scieszka, Jon.
The True Story of the 3 Little Pigs! New York: Puffin Books, 1989.

The story of the three pigs
is told from the point of view of the wolf.

After reading the three
versions of the Three Little Pigs, have children use a Venn diagram
to explore the similarities and differences among the various versions.
Identifying attributes and characteristics is an important part of algebraic
thinking.